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    "# Reference: https://jupyterbook.org/interactive/hiding.html\n",
    "# Use {hide, remove}-{input, output, cell} tags to hiding content\n",
    "\n",
    "import sys\n",
    "import os\n",
    "sys.path.append(os.path.abspath('../../..'))\n",
    "from textbook_utils import *"
   ]
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   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
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   "source": [
    "trees = pd.read_csv('data/black_spruce.csv')"
   ]
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   "execution_count": 3,
   "metadata": {
    "tags": [
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   "source": [
    "trees['status_0_1'] = 0 + (trees['status'] == 'fallen')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": [
     "remove-cell"
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   "source": [
    "splits = [4, 5, 6, 7, 8, 9, 10, 12, 14, 17, 20, 25, 32]\n",
    "tree_bins = (\n",
    "    trees[\"status_0_1\"]\n",
    "    .groupby(pd.cut(trees[\"diameter\"], splits))\n",
    "    .agg([\"mean\", \"count\"])\n",
    "    .rename(columns={\"mean\": \"proportion\"})\n",
    "    .assign(diameter=lambda df: [i.right for i in df.index])\n",
    ")"
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  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
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     "remove-cell"
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   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "trees['log_diam'] = np.log(trees['diameter']) \n",
    "X = trees[['log_diam']]\n",
    "y = trees['status_0_1']\n",
    "\n",
    "lr_model = LogisticRegression().fit(X, y)"
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    "# From Probabilities to Classification\n",
    "\n",
    "We started this chapter by presenting a binary classification problem where we want to model a nominal response variable. At this point, we have used logistic regression to model proportions or probabilities, and we're now ready to return to the original problem: we use the predicted probabilities to classify records. For our example, this means that for a tree of a particular diameter, we use the fitted coefficients from the logistic regression to estimate the chance it is fallen. If the chance is high, we classify a tree as fallen; otherwise, we classify it as standing. But we need to choose a threshold for making this *decision rule*."
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    "The `sklearn` logistic regression model's `predict` function implements the basic decision rule: predict `1` if the predicted probability $ p > 0.5 $. Otherwise, predict 0. We've overlaid this decision rule on top of the model predictions as a dotted line:"
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   ],
   "source": [
    "X_plt = pd.DataFrame(\n",
    "    {\"log_diam\": np.linspace(X[\"log_diam\"].min(), X[\"log_diam\"].max(), 50)}\n",
    ")\n",
    "p_hats = lr_model.predict_proba(X_plt)\n",
    "X_orig = np.exp(X_plt[\"log_diam\"])\n",
    "\n",
    "fig = px.scatter(\n",
    "    tree_bins, x=\"diameter\", y=\"proportion\", size=\"count\", log_x=True,\n",
    "    labels={\"diameter\": \"Tree diameter (cm)\", \"proportion\": \"Proportion down\"},\n",
    "    width=550, height=250,\n",
    ")\n",
    "\n",
    "fig.add_trace(go.Scatter(\n",
    "    x=X_orig, y=p_hats[:, 1], line=dict(color=\"orange\", width=3),\n",
    "    mode=\"lines\", name=\"Model predictions\",\n",
    "))\n",
    "\n",
    "fig.add_trace(go.Scatter(\n",
    "    x=X_orig, y=np.repeat(0.5, len(X_orig)),\n",
    "    line=dict(color=\"black\", width=3, dash=\"dashdot\"),\n",
    "    name=\"Decision rule\",\n",
    "))\n",
    "\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this section, we consider a more general decision rule. For some choice of $\\tau$, predict 1 if the model's predicted probability $ p > \\tau $, otherwise predict 0. By default, `sklearn` sets $ \\tau = 0.5 $. Let's explore what happens when $ \\tau $ is set to other values.\n",
    "\n",
    "Choosing an appropriate value for $\\tau$ depends on our goals. Suppose we want to maximize accuracy. The *accuracy* of a classifier is the fraction of correct predictions. We can compute the accuracy for different thresholds, meaning different $ \\tau $ values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def threshold_predict(model, X, threshold):\n",
    "    return np.where(model.predict_proba(X)[:, 1] > threshold, 1.0, 0.0)\n",
    "\n",
    "def accuracy(threshold, X, y):\n",
    "    return np.mean(threshold_predict(lr_model, X, threshold) == y)\n",
    "\n",
    "thresholds = np.linspace(0, 1, 200)\n",
    "accs = [accuracy(t, X, y) for t in thresholds]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To understand how accuracy changes with respect to $\\tau$, we make a plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
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   ],
   "source": [
    "fig = px.line(x=thresholds, y=accs, width=450, height=250)\n",
    "fig.add_trace(\n",
    "    go.Scatter(\n",
    "        x=[0.5, 0.5],\n",
    "        y=[0.3, 0.8],\n",
    "        mode=\"lines\",\n",
    "        name=\"𝛕 = 0.5\",\n",
    "        showlegend=True,\n",
    "    )\n",
    ")\n",
    "fig.update_xaxes(title=\"Threshold\")\n",
    "fig.update_yaxes(title=\"Accuracy\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the threshold with the highest accuracy isn't exactly at 0.5. In practice, we should use cross-validation to select the threshold (see {numref}`Chapter %s <ch:risk>`).\n",
    "\n",
    "The threshold that maximizes accuracy could be a value other than 0.5 for many reasons, but a common one is *class imbalance*, where one category is more frequent than another. Class imbalance can lead to a model that classifies a record as belonging to the more common category. In extreme cases (like fraud detection) when only a tiny fraction of the data contain a particular class, our models can achieve high accuracy by simply always predicting the frequent class without learning what makes a good classifier for the rare class. There are techniques for managing class imbalance, such as:\n",
    "\n",
    "+ Resampling the data to reduce or eliminate the class imbalance\n",
    "+ Adjusting the loss function to put a larger penalty on the smaller class\n",
    "\n",
    "In our example, the class imbalance is not that extreme, so we continue without these adjustments. \n",
    "\n",
    "The problem of class imbalance explains why accuracy alone is often not how we want to judge a model. Instead, we want to differentiate between the types of correct and incorrect classifications. We describe these next.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Confusion Matrix\n",
    "\n",
    "A convenient way to visualize errors in a binary classification is to look at the confusion matrix.  The confusion matrix compares what the model predicts with the actual outcomes. There are two types of error in this situation:\n",
    "\n",
    "*False-positives*\n",
    ": When the actual class is 0 (false) but the model predicts 1 (true)\n",
    "*False-negatives*\n",
    ": When the actual class is 1 (true) but the model predicts 0 (false)\n",
    "\n",
    "Ideally, we would like to minimize both kinds of errors, but we often need to manage the balance between these two sources."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ":::{note}\n",
    "\n",
    "The terms _positive_ and _negative_ come from disease testing, where a test indicates the presence of a disease, is called a positive result. This can be a bit confusing because having a disease doesn't seem like something positive at all. And $y=1$ denotes the \"positive\" case. To keep things straight, it's a good idea to confirm your understanding of what $y=1$ stands for in the context of your data.  \n",
    "\n",
    ":::"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`scikit-learn` has a function to compute and plot the confusion matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "       [104, 129]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix\n",
    "mat = confusion_matrix(y, lr_model.predict(X))\n",
    "mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "tags": [
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import plotly.figure_factory as ff\n",
    "\n",
    "fig = ff.create_annotated_heatmap(\n",
    "    z=mat,\n",
    "    x=[\"False\", \"True\"],\n",
    "    y=[\"False\", \"True\"],\n",
    "    showscale=False,\n",
    "    colorscale=px.colors.sequential.gray_r,\n",
    ")\n",
    "fig.update_layout(font=dict(size=16), width=300, height=250)\n",
    "\n",
    "# Add Labels\n",
    "fig.add_annotation(\n",
    "    x=0,\n",
    "    y=0,\n",
    "    text=\"True negative\",\n",
    "    yshift=30,\n",
    "    showarrow=False,\n",
    "    font=dict(color=\"white\", size=14),\n",
    ")\n",
    "fig.add_annotation(\n",
    "    x=1,\n",
    "    y=0,\n",
    "    text=\"False positive\",\n",
    "    yshift=30,\n",
    "    showarrow=False,\n",
    "    font=dict(color=\"black\", size=14),\n",
    ")\n",
    "fig.add_annotation(\n",
    "    x=0,\n",
    "    y=1,\n",
    "    text=\"False negative\",\n",
    "    yshift=30,\n",
    "    showarrow=False,\n",
    "    font=dict(color=\"black\", size=14),\n",
    ")\n",
    "fig.add_annotation(\n",
    "    x=1,\n",
    "    y=1,\n",
    "    text=\"True positive\",\n",
    "    yshift=30,\n",
    "    showarrow=False,\n",
    "    font=dict(color=\"black\", size=14),\n",
    ")\n",
    "\n",
    "fig.update_xaxes(title=\"Predicted\")\n",
    "fig.update_yaxes(title=\"Actual\", autorange=\"reversed\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ideally, we want to see all of the counts in the diagonal squares True Negative and True Positive. That means we have correctly classified everything. But this is rarely the case, and we need to assess the size of the errors. For this, it's easier to compare rates than counts. Next, we describe different rates and when we might prefer to prioritize one or the other.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Precision Versus Recall\n",
    "\n",
    "In some settings, there might be a much higher cost to missing positive cases.  For example, if we are building a classifier to identify tumors, \n",
    "we want to make sure that we don't miss any malignant tumors. Conversely, we're less concerned about classifying a benign tumor as malignant because a pathologist would still need to take a closer look to verify the malignant classification. In this case, we want to have a high true positive rate among the records that are actually positive. The rate is called *sensitivity*, or *recall*:\n",
    "\n",
    "$$\n",
    "\\text{Recall} = \\frac{\\text{True Positives}}{\\text{True Positives} + \\text{False Negatives}} = \\frac{\\text{True Positives}}{\\text{Actually True}}\n",
    "$$\n",
    "\n",
    "Higher recall runs the risk of predicting true on false records (false positives)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On the other hand, when classifying email as spam (positive) or ham (negative), we might be annoyed if an important email gets thrown into our spam folder. In this setting, we want high *precision*, the accuracy of the model for positive predictions:\n",
    "\n",
    "$$\n",
    "\\text{Precision} = \\frac{\\text{True Positives}}{\\text{True Positives} + \\text{False Positives}} = \\frac{\\text{True Positives}}{\\text{Predicted True}}\n",
    "$$\n",
    "\n",
    "Higher-precision models are often more likely to predict that true observations are negative (higher false-negative rate)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A common analysis compares the precision and recall at different thresholds:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import metrics\n",
    "precision, recall, threshold = (\n",
    "    metrics.precision_recall_curve(y, lr_model.predict_proba(X)[:, 1]))\n",
    "\n",
    "tpr_df = pd.DataFrame({\"threshold\":threshold, \n",
    "                       \"precision\":precision[:-1], \"recall\": recall[:-1], })"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To see how precision and recall relate, we plot them both against the threshold $ \\tau $:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
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   "source": [
    "fig = go.Figure()\n",
    "              \n",
    "fig.add_trace(go.Scatter(x=tpr_df[\"threshold\"], y=tpr_df[\"precision\"], name=\"Precision\"))\n",
    "\n",
    "fig.add_trace(go.Scatter(x=tpr_df[\"threshold\"], y=tpr_df[\"recall\"], name=\"Recall\",\n",
    "                         line=dict(dash='dash')))\n",
    "\n",
    "fig.update_layout(width=550, height=250, \n",
    "                  xaxis_title=\"Threshold\", yaxis_title=\"Proportion\")\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another common plot used to evaluate the performance of a classifier is the *precision-recall curve*, of PR curve for short. It plots the precision-recall pairs for each threshold:  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
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      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = px.line(tpr_df, x=\"recall\", y=\"precision\",\n",
    "             labels={\"recall\":\"Recall\",\"precision\":\"Precision\"})\n",
    "fig.update_layout(width=450, height=250, yaxis_range=[0, 1])\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the righthand end of the curve reflects the imbalance in the sample. The precision matches the fraction of fallen trees in the sample, 0.35. Plotting multiple PR curves for different models can be particularly useful for comparing models.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using precision and recall gives us more control over what kinds of errors matter.\n",
    "As an example, let's suppose we want to ensure that at least 75% of the fallen trees are classified as fallen. We can find the threshold where this occurs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {},
   "outputs": [],
   "source": [
    "fall75_ind = np.argmin(recall >= 0.75) - 1\n",
    "\n",
    "fall75_threshold = threshold[fall75_ind]\n",
    "fall75_precision = precision[fall75_ind]\n",
    "fall75_recall = recall[fall75_ind]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Threshold: 0.33\n",
      "Precision: 0.59\n",
      "Recall:    0.81\n"
     ]
    }
   ],
   "source": [
    "print(f'Threshold: {fall75_threshold:.2}')\n",
    "print(f'Precision: {fall75_precision:.2}')\n",
    "print(f'Recall:    {fall75_recall:.2}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We find that about 41% (1 – precision) of the trees that we classify as fallen are actually standing. In addition, we find the fraction of trees below this threshold to be:  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 252,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Proportion of samples below threshold: 0.52\n"
     ]
    }
   ],
   "source": [
    "print(\"Proportion of samples below threshold:\", \n",
    "      f\"{np.mean(lr_model.predict_proba(X)[:,1] < fall75_threshold):0.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, we have classified 52% of the samples as standing (negative). *Specificity* (also called *true negative rate*) measures the proportion of data belonging to the negative class that the classifier labels as negative:\n",
    "\n",
    "$$\n",
    "\\text{Specificity} = \\frac{\\text{True Negatives}}{\\text{True Negatives} + \\text{False Positives}} = \\frac{\\text{True Negatives}}{\\text{Predicted False}}\n",
    "$$\n",
    "\n",
    "The specificity for our threshold is: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "metadata": {},
   "outputs": [],
   "source": [
    "act_neg = (y == 0)\n",
    "true_neg = (lr_model.predict_proba(X)[:,1] < fall75_threshold) & act_neg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Specificity: 0.70\n"
     ]
    }
   ],
   "source": [
    "print(f\"Specificity: {np.sum(true_neg) / np.sum(act_neg):0.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In other words, 70% of the trees classified as standing are actually standing.\n",
    "\n",
    "As we've seen, there are several ways to use the 2-by-2 confusion matrix. Ideally, we want accuracy, precision, and recall to all be high. This happens when most predictions fall along the diagonal for the table, so our predictions are nearly all correct--true negatives and true positives. Unfortunately, in most scenarios our models will have some amount of error. In our example, trees of the same diameter include a mix of fallen and standing, so we can't perfectly classify trees based on their diameter. In practice, when data scientists choose a threshold, they need to consider their context to decide whether to prioritize precision, recall, or specificity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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